We review the recent progress in the field of multiferroic magnetoelectric heterostructures. The lack of single phase multiferroic candidates exhibiting simultaneously strong and coupled magnetic and ferroelectric orders led to an increased effort into the development of artificial multiferroic heterostructures in which these orders are combined by assembling different materials. The magnetoelectric coupling emerging from the created interface between the ferroelectric and ferromagnetic layers can result in electrically tunable magnetic transition temperature, magnetic anisotropy or magnetization reversal. The full potential of low energy consumption magnetic based devices for spintronics lies in our understanding of the magnetoelectric coupling at the scale of the ferroic domains. Although the thin film synthesis progresses resulted into the complete control of ferroic domain ordering using epitaxial strain, the local observation of magnetoelectric coupling remains challenging. The ability to imprint ferroelectric domains into ferromagnets and to manipulate those solely using electric fields suggests new technological advances for spintronics such as magnetoelectric memories or memristors.